The 25-year-old former Orlando Pirates, Monaco, Brugge and Westerlo frontman joined the Clarets in 2023.
Foster helped the side secure their place in the English Premier League on two occasions.
But he endured a difficult 2025/26 campaign as Burnley were relegated and also struggled to make an impact for South Africa at the 2026 World Cup.
He has now joined Houston with an option to join the club on a permanent transfer.
In total, Foster has spent four seasons with Burnley, making 89 league appearances and scoring 11 goals.
Club President Pat Onstad expressed his delight at the signing.
He told his club's website: "Lyle presents another powerful, mobile forward to our attacking group.
"He threatens the space behind the back line; links play well and brings the work rate and intensity that we demand without the ball.
“Lyle's experience in the Premier League and on the international stage will strengthen our group, and we are excited to welcome him to Houston as we prepare for a strong finish to the season.”
